1. Nov 3, 2014

### sergiokapone

If in the bottom of the bucket with water we made a hole, then water flows out of it. Bucket with water is the system with $m(t)$, thus we have to use equation:
$m(t)\frac{dv}{dt} = F + u\frac{dm}{dt}$.
Where $u\frac{dm}{dt}$ -- is jet reaction force.
But, I think the jet reaction force should not appear in this case. What is the solution of this paradox?

Last edited: Nov 3, 2014
2. Nov 3, 2014

### Danger

Hi, Sergio. If I understand the question correctly, there are two answers. A hole in the actually bottom would not provide thrust because the water would just be accelerating toward the ground as opposed to away from the bucket. That would lessen the effect of gravity upon the bucket because of weight loss, but that's not really a jet effect. If, on the other hand, the hole is in the side of the bucket near the bottom, there would be a tiny one because it would be pushing off from the water still in the container. I honestly think that I'm not correct in my interpretation of what you're asking though. Can you perhaps rephrase it?

3. Nov 3, 2014

### Staff: Mentor

I don't understand the question.

4. Nov 3, 2014

### sergiokapone

I do not completely understand this. How I can write the equation of motion in the case the bucket, which is on the floor?

5. Nov 3, 2014

### Danger

No help here... I don't know any math. I can say that there will be no motion at all if the thing is on the floor. (Unless you count immeasurably small structural vibrations on the molecular scale.) In fact, the water will just stop flowing completely if the surfaces of the bucket rim and the floor are smooth enough to form a seal.

Last edited: Nov 3, 2014
6. Nov 3, 2014

### sergiokapone

It is strange to me, the in the case of the rocket the outgoing propellant create jet forse, but in the case of bucket - whater is not.

7. Nov 3, 2014

### Danger

In the case of a rocket or air-breathing jet, or water jet or any other kind, the reaction mass is accelerated away from the container by either being expanded or being compressed and then released, or having the reaction chamber reduce in size to eject it (like in a syringe or balloon). In the bucket instance, gravity is simply pulling the water away from it. Earth is providing the force, not something in the bucket.

8. Nov 3, 2014

### A.T.

This is how a rocket produces thrust:

Where is the green force in the case of your bucket?

9. Nov 3, 2014

### sergiokapone

Ok, I understand that.

But now the quastion in the math. Why should I use equation of the motion $m(t)\frac{dv}{dt}=F$ instead $m(t)\frac{dv}{dt}=F + u\frac{dm}{dt}$? Is the $u$ -equal zero in this case? But, obviously it is not.

10. Nov 3, 2014

### A.T.

Define your symbols. What is F, v, m, u ?

11. Nov 3, 2014

### Danger

As mentioned, I don't know any math at all beyond simple geometry. What is "u"? If it's physical displacement on an x, y, or z axis, it is zero.

12. Nov 3, 2014

### sergiokapone

$u$ - is the propellant relative velocity (relative to rocket or some other thing, bucket, for example e.t.c.)

13. Nov 3, 2014

### A.T.

Velocity of what and when? What are the other symbols representing?

14. Nov 3, 2014

### sergiokapone

$u$ - is the propellant relative velocity
$F$ - external force, gravity force, for example
$v$ - is the velocity of the rocket
$m$ - is the current mass of the rocket

15. Nov 3, 2014

### Danger

Okay, but I rather suspect that the equation should apply only if there is some physical interaction between the two objects. In this case, there isn't. That would be like using it to determine the force between an aeroplane and canoe. What applies in your case is the gravity formula and how the bucket becomes lighter as water leaves it.

edit: You guys are posting too quickly for me to keep up with. I'm going to take a bathroom/TV break (it's the only room with a flatscreen) and I'll check in later.

Last edited: Nov 3, 2014
16. Nov 3, 2014

### sergiokapone

17. Nov 3, 2014

### A.T.

Okay, that should work for you bucket too.
Why not? If you make the hole to the side, it will create thrust an propel the bucket horizontally.

18. Nov 3, 2014

### sergiokapone

This is not interesting trivial case.
What if I will create the hole in the bottom?

19. Nov 3, 2014

### A.T.

Different direction of thrust.

20. Nov 3, 2014